Oscar Espinosa, Fabio Nieto
This research shows that under certain mathematical conditions, a threshold autoregressive model (TAR) can represent the leverage effect based on its conditional variance function. Furthermore, the analytical expressions for the third and fourth moment of the TAR model are obtained when it is weakly stationary.
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We propose a Bayesian nonparametric model including time-varying predictors in dynamic network inference. The model is applied to infer the dependence structure among financial markets during the global financial crisis, estimating effects of verbal and material cooperation efforts. We interestingly learn contagion effects, with increasing influence of verbal relations during the financial crisis and opposite results during the United States housing bubble.
Bayesian Dynamic Modeling of Realized Volatility in Financial Asset Price Forecasting
本文提出了一种新的贝叶斯动态模型，用于金融预测中的价格-实现波动率时间序列。通过将新的动态伽马过程模型与传统贝叶斯动态线性模型结合，改进了波动率杠杆和反馈效应的建模。
In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gaussian random vectors and are associated with the development of kernel methods. Bayesian optimization is an approach for performing derivative-free global optimization in a small dimension, and uses Gaussian processes to locate the global maximum of a black-box function. The firs…
Bayesian Models for Joint Selection of Features and Auto-Regressive Lags: Theory and Applications in Environmental and Financial Forecasting
本文提出一种基于spike-and-slab先验的分层贝叶斯框架，用于线性回归中协变量与滞后误差项的联合选择，并设计两阶段MCMC算法解决高维计算问题，在理论和实际应用中均展现出更高的选择准确性与预测性能。
This paper estimates models of high frequency index futures returns using `around the clock' 5-minute returns that incorporate the following key features: multiple persistent stochastic volatility factors, jumps in prices and volatilities, seasonal components capturing time of the day patterns, correlations between return and volatility shocks, and announcement effects. We develop an integrated MCMC approach to estimate interday and intraday parameters and states using high-frequency data without resorting to various aggregation measures like realized volatility. We provide a case study using …
Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A Lévy process with infinite jump activity and microstructure noise is considered one of the simplest, yet accurate enough, models for financial data at high-frequency. Utilizing this model, we propose a "purposely misspecified" posterior of the volatility obtained by ignoring the jump-component of the process. The misspecified posterior is further corrected by a simple estimate of the location shift and re-scaling of the log likelihood. Our main result establishes a Bernst…
Do financial regulators act in the public's interest? A Bayesian latent class estimation framework for assessing regulatory responses to banking crises
本文提出贝叶斯潜在类别估计框架，基于维护金融稳定与抑制道德风险的双重目标评估银行监管机构在危机中的处置决策，发现80年代美国银行业监管符合理论建议而S&L监管机构偏离建议导致纳税人损失132亿美元。
Scenario Analysis with Multivariate Bayesian Machine Learning Models
本文提出利用多变量贝叶斯机器学习模型进行情景分析，通过压力测试情景预测、宏观经济风险评估和金融冲击的非对称效应研究，揭示了非线性和不对称性的重要性。
The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and embedding a novel, adaptive method of simultaneous predictor selection in forward filtering for on-line learning and forecasting. The advances include developments in Bayesian computation for scalability, and a case study in exploring the resulting potential for improved short-term forecasting of large-scale volatility matrices. A case study co…
Banks and financial institutions all over the world manage portfolios containing tens of thousands of customers. Not all customers are high credit-worthy, and many possess varying degrees of risk to the Bank or financial institutions that lend money to these customers. Hence assessment of credit risk is paramount in the field of credit risk management. This paper discusses the use of Bayesian principles and simulation-techniques to estimate and calibrate the default probability of credit ratings. The methodology is a two-phase approach where, in the first phase, a posterior density of default …
News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable estimation of the model's parameters, detection of jumps and analysis of jump frequency. The methodology, founded upon the idea of latent variables, is illustrated with two empirical studies, employing both simulated and real-world data (the KGHM index). News might trigger jump arri…
As the dynamic structure of the financial markets is subject to dramatic changes, a model capable of providing consistently accurate volatility estimates must not make strong assumptions on how prices change over time. Most volatility models impose a particular parametric functional form that relates an observed price change to a volatility forecast (news impact function). We propose a new class of functional coefficient semiparametric volatility models where the news impact function is allowed to be any smooth function, and study its ability to estimate volatilities compared to the well known…
A new Bayesian significance test is adjusted for jump detection in a diffusion process. This is an advantageous procedure for temporal data having extreme valued outliers, like financial data, pluvial or tectonic forces records and others.
Bayesian Predictive Decision Synthesis
该研究提出贝叶斯预测决策综合（BPDS）方法，以决策导向视角拓展模型不确定性研究，通过新颖的主观贝叶斯模型加权视角，将决策分析结果整合到多模型评估比较中，并在回归设计、金融预测等场景验证了有效性。
Misperceptions about extreme dependencies between different financial assets have been an im- portant element of the recent financial crisis. This paper studies inhomogeneity in dependence structures using Markov switching regular vine copulas. These account for asymmetric depen- dencies and tail dependencies in high dimensional data. We develop methods for fast maximum likelihood as well as Bayesian inference. Our algorithms are validated in simulations and applied to financial data. We find that regime switches are present in the dependence structure of various data sets and show that regime…
Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of occurrences of new events depend on the past of the process is the Hawkes process. In this work we consider the nonlinear Hawkes process, which notably models excitation and inhibition phenomena between dimensions of the process. In a nonparametric Bayesian estimation framework, we obtain concentration rates of the posterior distribution on the parameters, u…
Predicting Stock Market Crash with Bayesian Generalised Pareto Regression
本文提出贝叶斯广义帕累托回归模型，结合波动率协变量预测印度Nifty 50指数崩盘风险，实证表明Cauchy先验最优且全球波动率显著提升预测能力。
Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market variability. However we can achieve significantly better insight by considering the time-varying analogues of these models. In this paper, we propose a Bayesian approach to the estimation of such models and develop computationally efficient MCMC algorithm based on Hamiltonian Monte Carlo (HMC) sampling. We also established posterior contraction rates with incre…
The prediction of financial markets is a challenging yet important task. In modern electronically-driven markets, traditional time-series econometric methods often appear incapable of capturing the true complexity of the multi-level interactions driving the price dynamics. While recent research has established the effectiveness of traditional machine learning (ML) models in financial applications, their intrinsic inability to deal with uncertainties, which is a great concern in econometrics research and real business applications, constitutes a major drawback. Bayesian methods naturally appear…
Modeling of Measurement Error in Financial Returns Data
针对基金收益数据测量误差建模中联合转移密度难获取、难精确模拟的问题，基于断棍表示构建Lévy过程驱动的近似随机模型，提出多层MCMC算法以降低贝叶斯后验推断的计算成本，并在多场景含真实数据中验证。
Continuous time Bayesian networks are investigated with a special focus on their ability to express causality. A framework is presented for doing inference in these networks. The central contributions are a representation of the intensity matrices for the networks and the introduction of a causality measure. A new model for high-frequency financial data is presented. It is calibrated to market data and by the new causality measure it performs better than older models.
Value-at-Risk (VaR) and Expected Shortfall (ES) are widely used in the financial sector to measure the market risk and manage the extreme market movement. The recent link between the quantile score function and the Asymmetric Laplace density has led to a flexible likelihood-based framework for joint modelling of VaR and ES. It is of high interest in financial applications to be able to capture the underlying joint dynamics of these two quantities. We address this problem by developing a hybrid model that is based on the Asymmetric Laplace quasi-likelihood and employs the Long Short-Term Memory…
Bayesian Portfolio Optimization by Predictive Synthesis
针对金融市场不确定性导致单一预测模型失效的问题，提出基于贝叶斯预测合成（BPS）的投资组合优化方法，通过动态线性模型组合多个资产收益预测，构建均值-方差和分位数投资组合。
Posterior Uncertainty for Targeted Parameters in Bayesian Bootstrap Procedures
本文提出了一种广义的链接贝叶斯抽样方法，用于处理贝叶斯抽样中目标参数的后验不确定性，具有良好的频繁性质和可信区间覆盖性。
The Net Promoter Score is a simple measure used by several companies as indicator of customer loyalty. Studies that address the statistical properties of this measure are still scarce and none of them considered the sample size determination problem. We adopt a Bayesian approach to provide point and interval estimators for the Net Promoter Score and discuss the determination of the sample size. Computational tools were implemented to use this methodology in practice. An illustrative example with data from financial services is also presented.
A Latent Class Bayesian Model for Multivariate Longitudinal Outcomes with Excess Zeros
该研究提出一种面向含过多零值的多变量纵向结果的贝叶斯潜类别模型，结合不同零膨胀结果的对应模型与自适应Lasso变量选择，经真实数据与模拟验证有效。
Bayesian Hierarchical Copula Models with a Dirichlet-Laplace Prior
本文针对金融时间序列聚类提出贝叶斯分层copula模型，采用Dirichlet-Laplace全局-局部收缩先验解决后验不适定问题并刻画聚类间依赖，通过模拟和真实数据验证性能。
In this article we consider Bayesian inference for partially observed Andersson-Madigan-Perlman (AMP) Gaussian chain graph (CG) models. Such models are of particular interest in applications such as biological networks and financial time series. The model itself features a variety of constraints which make both prior modeling and computational inference challenging. We develop a framework for the aforementioned challenges, using a sequential Monte Carlo (SMC) method for statistical inference. Our approach is illustrated on both simulated data as well as real case studies from university gradua…
Posterior Regimes and Latent Deception: Variational Bayesian Inference in Hidden Markov Models for Sequential Fraud Detection in Financial Transactions
本文提出三层隐马尔可夫模型（最大似然、变分贝叶斯、神经变分）用于金融交易序列欺诈检测，通过潜在状态识别欺诈，并指出后验概率常被误用，提出校准的分诊层而非直接替代排序模型。
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be inaccurate when there are covariates that could have a large influence on the dependence structure of the data. To account for this, a Bayesian framework for the estimation of conditional copulas is proposed. In this framework the parameters of a copula are non-linearly related to some arbitrary conditioning variables. We e…
We discuss the Bayesian emulation approach to computational solution of multi-step portfolio studies in financial time series. "Bayesian emulation for decisions" involves mapping the technical structure of a decision analysis problem to that of Bayesian inference in a purely synthetic "emulating" statistical model. This provides access to standard posterior analytic, simulation and optimization methods that yield indirect solutions of the decision problem. We develop this in time series portfolio analysis using classes of economically and psychologically relevant multi-step ahead portfolio uti…
Target encoding is an effective encoding technique of categorical variables and is often used in machine learning systems for processing tabular data sets with mixed numeric and categorical variables. Recently en enhanced version of this encoding technique was proposed by using conjugate Bayesian modeling. This paper presents a further development of Bayesian encoding method by using sampling techniques, which helps in extracting information from intra-category distribution of the target variable, improves generalization and reduces target leakage.
We propose a Bayesian non-parametric approach for modeling the distribution of multiple returns. In particular, we use an asymmetric dynamic conditional correlation (ADCC) model to estimate the time-varying correlations of financial returns where the individual volatilities are driven by GJR-GARCH models. The ADCC-GJR-GARCH model takes into consideration the asymmetries in individual assets' volatilities, as well as in the correlations. The errors are modeled using a Dirichlet location-scale mixture of multivariate Gaussian distributions allowing for a great flexibility in the return distribut…
This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distributions. A diagonal matrix of discount factors is employed in order to discount the variances element by element and therefore allowing a flexible and pragmatic variance modelling approach. Diagnostic tests and sequential model monitoring are discussed in some detail. The proposed …
This paper introduces a feasible and practical Bayesian method for unit root testing in financial time series. We propose a convenient approximation of the Bayes factor in terms of the Bayesian Information Criterion as a straightforward and effective strategy for testing the unit root hypothesis. Our approximate approach relies on few assumptions, is of general applicability, and preserves a satisfactory error rate. Among its advantages, it does not require the prior distribution on model's parameters to be specified. Our simulation study and empirical application on real exchange rates show g…
We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, which constitutes the solution to the tracking problem, as well as the model parameters. In the numerical section, we present performance comparisons with several competing techniques and demonstrate significant performance improvements in all cases.
With the increasing variety of services that e-commerce platforms provide, criteria for evaluating their success become also increasingly multi-targeting. This work introduces a multi-target optimization framework with Bayesian modeling of the target events, called Deep Bayesian Multi-Target Learning (DBMTL). In this framework, target events are modeled as forming a Bayesian network, in which directed links are parameterized by hidden layers, and learned from training samples. The structure of Bayesian network is determined by model selection. We applied the framework to Taobao live-streaming …
A method to predict time-series using multiple deep learners and a Bayesian network is proposed. In this study, the input explanatory variables are Bayesian network nodes that are associated with learners. Training data are divided using K-means clustering, and multiple deep learners are trained depending on the cluster. A Bayesian network is used to determine which deep learner is in charge of predicting a time-series. We determine a threshold value and select learners with a posterior probability equal to or greater than the threshold value, which could facilitate more robust prediction. The…
In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian approach. The present paper extends this work for selecting the most appropriate rule base among a set of competing alternatives, which best explains the data, by calculating the model evidence or marginal likelihood. We explain why this is an attractive alternative over simply minimizing a mean squared error metric of prediction and show the validity of the propos…
We propose a new Bayesian Markov switching regression model for multidimensional arrays (tensors) of binary time series. We assume a zero-inflated logit regression with time-varying parameters and apply it to multilayer temporal networks. The original contribution is threefold. First, to avoid over-fitting we propose a parsimonious parametrization based on a low-rank decomposition of the tensor of regression coefficients. Second, we assume the parameters are driven by a hidden Markov chain, thus allowing for structural changes in the network topology. We follow a Bayesian approach to inference…
Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the sequential learning of volatility state variables and parameters, whereby the investor must update all posterior and predictive densities as new information arrives. We develop a particle filtering and learning algorithm to sample posterior distribution in Merton's jump stochastic volatility. This allows to filter spot volatilities and jump times, together with se…
Bayesian Joint Estimation of the Hurst Parameter and Volatility with Applications to Fractional Option Pricing
提出贝叶斯框架联合估计分数随机微分方程中的赫斯特参数和波动率，将后验不确定性传播到期权定价，通过模拟和原油数据验证了方法的稳定性和实用性。
We propose a multinomial logistic regression model for link prediction in a time series of directed binary networks. To account for the dynamic nature of the data we employ a dynamic model for the model parameters that is strongly connected with the fused lasso penalty. In addition to promoting sparseness, this prior allows us to explore the presence of change points in the structure of the network. We introduce fast computational algorithms for estimation and prediction using both optimization and Bayesian approaches. The performance of the model is illustrated using simulated data and data f…
Typical Bayesian inference requires parameter identification via likelihood parameterization, which has invited criticism for being less flexible than the Frequentist framework and subject to misspecification. Though misspecification may be avoided by functional parameter inference under a nonparametric model space, there does not exist a flexible Bayesian semiparametric model that would allow full control over the marginal prior over any general functional parameter. We present the technique of $θ$-augmentation which helps us manipulate nonparametric models into semiparametric ones that direc…
Pair-copula Bayesian networks (PCBNs) are a novel class of multivariate statistical models, which combine the distributional flexibility of pair-copula constructions (PCCs) with the parsimony of conditional independence models associated with directed acyclic graphs (DAG). We are first to provide generic algorithms for random sampling and likelihood inference in arbitrary PCBNs as well as for selecting orderings of the parents of the vertices in the underlying graphs. Model selection of the DAG is facilitated using a version of the well-known PC algorithm which is based on a novel test for con…
Modelling financial volume curves with hierarchical Poisson processes
本文提出基于分层狄利克雷过程的分层泊松过程模型，对股票日内成交量曲线进行非参数贝叶斯建模，并推导高效MCMC算法，在NASDAQ高流动性股票数据上验证了方法的可扩展性。
Managing risk at the aggregate level is crucial for banks and financial institutions as required by the Basel III framework. In this paper, we introduce discrete time Bayesian state space models with Poisson measurements to model aggregate mortgage default rate. We discuss parameter updating, filtering, smoothing, forecasting and estimation using Markov chain Monte Carlo methods. In addition, we investigate the dynamic behavior of the default rate and the effects of macroeconomic variables. We illustrate the use of the proposed models using actual U.S. residential mortgage data and discuss ins…
In this paper we propose a novel approach for learning from data using rule based fuzzy inference systems where the model parameters are estimated using Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. We show the applicability of the method for regression and classification tasks using synthetic data-sets and also a real world example in the financial services industry. Then we demonstrate how the method can be extended for knowledge extraction to select the individual rules in a Bayesian way which best explains the given data. Finally we discuss the advantages and pitfalls …
Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying sparsity pattern is fixed. We propose here an original class of flexible Bayesian linear models for dynamic sparsity modelling. The proposed class of models expands upon the existing Bayesian literature on sparse regression using generalized multivariate hyperbolic distributions. The…
Advances in Bayesian Modeling: Applications and Methods
本文综合 MCMC 与变分近似，系统展示贝叶斯建模在多领域的建模、先验获取、计算及评估方法。
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bayesian inference of sparse structures of Gaussian graphical models (GGMs). One is based on a simple modification of the cutting-edge block Gibbs sampler for sparse GGMs, which results in significant computational gains in high dimensions. The other method is based on a specific co…
We propose a novel Dirichlet-based Pólya tree (D-P tree) prior on the copula and based on the D-P tree prior, a nonparametric Bayesian inference procedure. Through theoretical analysis and simulations, we are able to show that the flexibility of the D-P tree prior ensures its consistency in copula estimation, thus able to detect more subtle and complex copula structures than earlier nonparametric Bayesian models, such as a Gaussian copula mixture. Further, the continuity of the imposed D-P tree prior leads to a more favorable smoothing effect in copula estimation over classic frequentist metho…
Approximate Bayesian computation (ABC), also known as likelihood-free methods, have become a favourite tool for the analysis of complex stochastic models, primarily in population genetics but also in financial analyses. We advocated in Grelaud et al. (2009) the use of ABC for Bayesian model choice in the specific case of Gibbs random fields (GRF), relying on a sufficiency property mainly enjoyed by GRFs to show that the approach was legitimate. Despite having previously suggested the use of ABC for model choice in a wider range of models in the DIY ABC software (Cornuet et al., 2008), we prese…
Cointegration is an important concept in the analysis of non-stationary time-series, giving conditions under which a collection of non-stationary processes has an underlying stationary (cointegration) relationship. In this paper we present the first fully Bayesian residual-based test for cointegration, where we consider the whole space of possible cointegration relationships when testing for the presence of cointegration. We first demonstrate that such a test can be performed exactly in the case where the residual process follows a first-order autoregressive process. We then extend this test t…
Bayesian Nonlinear Regression using Sums of Simple Functions
本文提出一种基于简单双组分位置混合模型求和的贝叶斯非线性回归方法，利用逻辑函数刻画组分转换，结合共轭先验实现高效推断，并在模拟和美国宏观经济预测及大规模非线性VAR中验证了其准确性与捕捉非线性效应的能力。
We propose and evaluate an iterative localization mechanism employing Bayesian inference to estimate the position of a target using received signal strength measurements. The probability density functions of the target's coordinates are estimated through a Bayesian network. Herein, we consider an iterative procedure whereby our predictor (posterior distribution) is updated in a sequential order whenever new measurements are made available. The performance of the mechanism is assessed in terms of the respective root mean square error and kernel density estimation of the target coordinates. Our …
In many real-world scenarios where data is high dimensional, test time acquisition of features is a non-trivial task due to costs associated with feature acquisition and evaluating feature value. The need for highly confident models with an extremely frugal acquisition of features can be addressed by allowing a feature selection method to become target aware. We introduce an approach to feature selection that is based on Bayesian learning, allowing us to report target-specific levels of uncertainty, false positive, and false negative rates. In addition, measuring uncertainty lifts the restrict…
We find empirical evidence that mean-reverting jump processes are not statistically adequate to model electricity spot price spikes but independent, signed sums of such processes are statistically adequate. Further we demonstrate a change in the composition of these sums after a major economic event. This is achieved by developing a Markov Chain Monte Carlo (MCMC) procedure for Bayesian model calibration and a Bayesian assessment of model adequacy (posterior predictive checking). In particular we determine the number of signed mean-reverting jump components required in the APXUK and EEX market…
To answer the call of introducing more Bayesian techniques to organizational research (e.g., Kruschke, Aguinis, & Joo, 2012; Zyphur & Oswald, 2013), we propose a Bayesian approach for meta-analysis with power prior in this article. The primary purpose of this method is to allow meta-analytic researchers to control the contribution of each individual study to an estimated overall effect size though power prior. This is due to the consideration that not all studies included in a meta-analysis should be viewed as equally reliable, and that by assigning more weights to reliable studies with power …
Bayesian Rao test for distributed target detection in interference and noise with limited training data
本文针对训练数据有限条件下干扰与噪声中的距离扩展目标检测问题，提出基于逆Wishart先验和Rao检验的贝叶斯检测器，并通过仿真与实测数据验证其性能优于现有方法。
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